USP 3,957,786 (corresponding to German Specification 1,942,405) concerns piperazinylalkylaminouracils (and their salts with inorganic or organic acids) which exhibit hypotensive activity superior to that of previously-known antihypertensive agents. Of the compounds actually named therein, exploratory clinical testing established that the title compound of Example 4, 1,3-dimethyl-4-(.gamma.-[4-(o-methoxyphenyl)piperazinyl( 1)]-propylamino)uracil (urapidil), is particularly well suited for treating hypertension. However, further testing revealed that urapidil therapy achieved blood-pressure normalization in only about half of the patients with essential and secondary hypertension (of different degrees of gravity) to whom it was administered. At the same time, the compatibility of this hypotensive agent failed to fulfil all expectations. A product yielding a higher rate of blood-pressure normalization is required for wide therapeutic application.